Question

If the zeroes of the polynomial $5x^2-7x+k$ are reciprocal of each other, then find the value of $k$.

Answer 1

Zeros of the polynomial are the roots of this quadratc equation $5x^2-7x+k=0$

Given that the roots re reciprocal of each other. Hence product of roots will be $1$

From the given equation we can see that product of the roots $=\frac{k}{5}$

$\Rightarrow \frac{k}{5}=1$

$\Rightarrow k=5$